Question: Reduce to lowest terms: $ \dfrac{5}{7} \div \dfrac{4}{9} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{4}{9}$ is $ \dfrac{9}{4}$ Therefore: $ \dfrac{5}{7} \div \dfrac{4}{9} = \dfrac{5}{7} \times \dfrac{9}{4} $ $ \phantom{ \dfrac{5}{7} \times \dfrac{9}{4}} = \dfrac{5 \times 9}{7 \times 4} $ $ \phantom{ \dfrac{5}{7} \times \dfrac{9}{4}} = \dfrac{45}{28} $